General Version of Gauss-type Proximal Point Method and Its Uniform Convergence Analysis for Metrically Regular Mappings
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 20, Issue 4
Abstract
We study the uniform convergence of the general version of Gauss-type proximal point algorithm (GG-PPA), introduced by Alom et al. [1], for solving the parametric generalized equations y ∈ T(x), where T : X 2Y is a set-valued mapping with locally closed graph, y is a parameter, and X and Y are Banach spaces. In particular, we establish the uniform convergence of the GG-PPA by considering a sequence of Lipschitz continuous functions gk : X → Y with gk(0) = 0 and positive Lipschitz constants k in the sense that it is stable under small perturbations when T is metrically regular at a given point. In addition, we give a numerical example to justify the uniform convergence of the GG-PPA.
Authors and Affiliations
M. A. Alom, M. H. Rashid, K. K. Dey
Keywords
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- EP ID EP322543
- DOI 10.9734/BJMCS/2017/31193
- Views 92
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